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An exotic menagerie. (English) Zbl 0808.57012

In a quest to further demonstrate the perversities that occur in dimension four, the author describes further interesting constructions of uncountably many exotic smooth structures on \(\mathbb{R}^ 4\) and other open 4-manifolds. In particular, the author shows that for any topological 4- manifold \(M\), \(M\)-pt. admits uncountably many smoothings. He then goes on to explicitly construct exotic smooth structures on \(\mathbb{R}^ 4\). Finally, he deftly compares and relates the various constructions of these exotic \(\mathbb{R}^ 4\).

MSC:

57N13 Topology of the Euclidean \(4\)-space, \(4\)-manifolds (MSC2010)
57R55 Differentiable structures in differential topology
57R57 Applications of global analysis to structures on manifolds
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